Identify the graph that correctly represents the inequality |x + 1| + 2 > 5.
2 answers:
The greater than 3 means that the graph will have a shaded region for when the absolute value of (x+1) is greater than 3.
The absolute value means that we are interested in the magnitude of x+1. That means that the the graph will be shaded where x+1 > 3, and where -x-1 > 3
If we solve both of these for x, we get:
x > 2 and x < -4
So the graph will look like the attached picture. Notice that the vertical lines are dotted rather than solid. This means that we are dealing with a greater than sign, not a greater than or equal to.
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Answer:
Step-by-step explanation:
Use the slope-intercept form:
m is the slope and b is the y-intercept. Looking at the graph, you can find the y-intercept. The y-intercept is the point where x equals 0:
To find the slope, take any two points from the line:
Use the slope formula for when you have two points:
The rise over run is the change in the y-axis over the change of the x-axis. Insert the appropriate values:
Simplify parentheses (two negatives makes a positive):
Simplify (two negatives make a positive):
The slope is and the y-intercept is
. Insert these into the equation:
Finito.